STUDY OF H_∞ CONTROL THEORY AND ITS APPLICATIONS

Robust control on linear uncertain system has attracted more and more attention from specialists and scholars in the control field recently. Based on the research results about Linear Matrix Inequality(LMI) and Structure Singular Value (SSV), this dissertation presents problems about robust stability and robust controller design of linear uncertain system. The main contributions are given as follows:1.Discussed the description of uncertain system, and Studied the robust control problem with real uncertainty system, as well as derived robust stability conditions of nonstructure uncertainty system based on small gain theorem. Related algorithms mentioned above are given.2.Studied the structure singular value theory in the paper, and also discussed robust stability and robust performance in uncertain block system via structure singular value. As simulation sample applied its to a spacecraft controller, the result show efficiency of SSV algorithm.3.The problem of robust controller design in time domain by reducing to the solving of linear matrix inequality is studied in this dissertation, two methods for robust controller design based on LMI approach are presented here. One is feedback controller design, and the other is observer-based controller design.4.The reduced order filter design for continuous and discrete system is put forward based on linear matrix inequality, and a set of permitted filters are obtained.5.The technique of H~ controller design via graph-- H~ loop shape is studied, and the basic steps of loop shape design is provided.6.The given approaches on robust controller and filter are applied in a torpedo control system .The simulations show its efficiency and feasibility.